1 /* $OpenBSD: s_ctanl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */
4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
6 * Permission to use, copy, modify, and distribute this software for any
7 * purpose with or without fee is hereby granted, provided that the above
8 * copyright notice and this permission notice appear in all copies.
10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
21 * Complex circular tangent
27 * long double complex ctanl();
28 * long double complex z, w;
42 * w = --------------------.
45 * On the real axis the denominator is zero at odd multiples
46 * of PI/2. The denominator is evaluated by its Taylor
47 * series near these points.
53 * arithmetic domain # trials peak rms
54 * DEC -10,+10 5200 7.1e-17 1.6e-17
55 * IEEE -10,+10 30000 7.2e-16 1.2e-16
56 * Also tested by ctan * ccot = 1 and catan(ctan(z)) = z.
63 #if LDBL_MANT_DIG == 64
64 static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
65 #elif LDBL_MANT_DIG == 113
66 static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
69 static const long double PIL = 3.141592653589793238462643383279502884197169L;
70 static const long double DP1 = 3.14159265358979323829596852490908531763125L;
71 static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L;
72 static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L;
75 redupil(long double x)
86 i = t; /* the multiple */
88 t = ((x - t * DP1) - t * DP2) - t * DP3;
93 ctansl(long double complex z)
95 long double f, x, x2, y, y2, rn, t;
98 x = fabsl(2.0L * creall(z));
99 y = fabsl(2.0L * cimagl(z));
131 while (fabsl(t/d) > MACHEPL);
136 ctanl(long double complex z)
138 long double complex w;
143 d = cosl(2.0L * x) + coshl(2.0L * y);
145 if (fabsl(d) < 0.25L) {
150 /*mtherr( "ctan", OVERFLOW );*/
151 w = LDBL_MAX + LDBL_MAX * I;
155 w = sinl(2.0L * x) / d + (sinhl(2.0L * y) / d) * I;